Question

Find the cube root of 512.

Answer 1

Hint: To find the cube root, we write 512 as multiples of prime numbers and solve it to get its value. As it is an even number, it is definitely divisible by 2, so we start off by writing it as multiples of 2.

Complete step-by-step answer:

Given Data, cube root of 512
$ \Rightarrow \sqrt[3]{{512}} = {\left( {512} \right)^{\dfrac{1}{3}}}$
Now 512 = $
  \left( {2 \times 256} \right) = \left( {2 \times 2 \times 128} \right) = \left( {2 \times 2 \times 2 \times 64} \right) \\
   \Rightarrow \left( {\left( {2 \times 2 \times 2} \right) \times \left( {2 \times 2 \times 2} \right) \times \left( {2 \times 2 \times 2} \right)} \right) \\
$
⟹Cube root of 512 = $\sqrt[3]{{512}} = {\left( {512} \right)^{\dfrac{1}{3}}} = {2^9}$
⟹${\left( {{2^9}} \right)^{\dfrac{1}{3}}} = {2^3} = 8$
Hence, the cube root of 512 is 8.

Note: In order to solve this type of questions the key concept is to identify cube root of a number is that number raised to a power of$\dfrac{1}{3}$, then write the given number in form of a prime number or multiple of prime numbers raised to some power. Then we compute it to get the answer.